What if you don’t want to run Linux on your smartphone or your device is not supported, but still want to have (some) control over your apps and data? This is another incomplete Android tweaking guide, focused on replacing pre-installed/popular apps with powerful open-source alternatives.

If you have already used F-Droid before, you can skip this paragraph. F-Droid is an app that works as a catalogue of apps, similar to Google Play. You will not find it in Play, you have to download it from the official website and install it, similarly to installing a program in Windows. After that, you can browse and install apps the convenient way. The difference is that everything in there is open-source and ad-free, designed for privacy-conscious users. The following list consists of apps uploaded in F-Droid, but some of them are also available in Google Play.
I have not tested them in all Android flavours and often only some versions are supported; it’s a trial and error process to find the one for each category. If you search for a desired operation you will find a few options to choose between lightness, elegance and practicality. This is a personal-recommendation-list, not a definitely-best-for-you-list.

Web browsingFirefox instead of Chrome.
The debate for the perfect browser is out of scope here, but obviously your browser is one of the things you will consider changing. (Yes, there are alternatives to Firefox.)

YouTube browsingNewPipe instead of YouTube.
NewPipe is a front-end for YouTube, basically YouTube with privacy and without ads. It can also play in the background (!) if you like. Since, PeerTube is not always enough, no matter how substantial.

VPNOrbot to access the Tor network.Tor is not really a VPN, but this app works mostly as a VPN. No need for access to specific (paid) servers.

Directory ExplorationSimple File Manager Pro to view and handle directories.
Google’s Files are designed to show only files saved directly from the user. Finding system folders is not that simple. The Simple File Manager belongs to a series of apps for basic operations by Simple Mobile Tools, most of which are worth trying. The apps require a payment in Google Play, so they are not Free anymore. Yet, you can still install open-source versions via F-Droid, without payments or ads.

Chat, Messaging, Collaboration
Unless, you didn’t land here from mastodon, you already know how to survive without Facebook. A few ideas for encrypted communications:Signal, end-to-end encrypted chatTelegram, client-server encrypted chat with limited end-to-end encryption capabilitiesBriar, peer-to-peer encrypted chat with offline communication capabilitiesRiot, chat and collaboration tool based on Matrix with optional end-to-end encryptionAntox for Tox, end-to-end encrypted chat and collaboration tool, now in alpha
Some of those tools require a phone number to set up, making them not ideal for anonymity.

Notes:

Limiting permissions or even disabling remaining system apps might make you feel safer, although some of them are necessary for your phone to function properly.

If you still use proprietary apps, you can try Exodus Privacy to monitor their behaviour, or AdAway (requires Root access) to block built-in ads.

One step further: try Private Location to spoof your location, Scrambled Exif to remove camera metadata from images and PilferShush Jammer to block apps from secretly using your microphone (my testing was inadequate to prove that these 3 apps actually make a difference).